A Bivariate Normal Inverse Gaussian Process with Stochastic Delay: Efficient Simulations and Applications to Energy Markets

Using the concept of self-decomposable subordinators introduced by Gardini, Sabino, and Sasso, we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme that relies on the mathematical connection between self-decomposable Inverse Gaussian laws and Lévy-driven Ornstein–Uhlenbeck processes with Inverse Gaussian stationary distribution. We show that our approach provides an improvement to the existing simulation scheme detailed in Zhang and Zhang, because it does not rely on an acceptance–rejection method. Eventually, these results are applied to the modelling of energy markets and to the pricing of spread options using the proposed Monte Carlo scheme and Fourier techniques.